(please ignore the full stops)
details:
if the distance from S to F (hypotenuse) , passing through X =200(secY + sec Z)
and tanY + tanZ=5/2
and the distance from S to F, passing through X in terms of Y=200(secY + 0.5(4sec^2Y - 20tanY+25)^(1/2)

if an object can travel 4m/s through sand and 3m/s through mud, determine the best route it should travel through to get from S to F (hypotenuse), passing through X. and the time taken

(please ignore the full stops)
details:
if the distance from S to F (hypotenuse) , passing through X =200(secY + sec Z)
and tanY + tanZ=5/2
and the distance from S to F, passing through X in terms of Y=200(secY + 0.5(4sec^2Y - 20tanY+25)^(1/2)

if an object can travel 4m/s through sand and 3m/s through mud, determine the best route it should travel through to get from S to F (hypotenuse), passing through X. and the time taken

I think you will find everything you need to do this in the answers to your
earlier question here